Geometric vs. Binomial

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials needed to get the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.

Front

What is a binomial distribution?

Back

A binomial distribution represents the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is the probability of success in a geometric distribution?

Back

The probability of success in a geometric distribution is denoted as 'p' and is constant for each trial.

Front

What is the formula for the probability of getting the first success on the k-th trial in a geometric distribution?

Back

P(X = k) = (1 - p)^(k-1) * p, where p is the probability of success.

Front

What is the expected value of a geometric distribution?

Back

The expected value (mean) of a geometric distribution is E(X) = 1/p.

Tags

CCSS.HSS.MD.A.2

Front

What is the variance of a geometric distribution?

Back

The variance of a geometric distribution is Var(X) = (1 - p) / p^2.

Front

What is the probability of getting exactly k successes in n trials in a binomial distribution?

Back

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where 'n' is the number of trials and 'p' is the probability of success.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the expected value of a binomial distribution?

Back

The expected value (mean) of a binomial distribution is E(X) = n * p.

Tags

CCSS.HSS.MD.A.2

Front

What is the variance of a binomial distribution?

Back

The variance of a binomial distribution is Var(X) = n * p * (1 - p).

Front

How do you determine if a situation can be modeled by a geometric distribution?

Back

A situation can be modeled by a geometric distribution if you are counting the number of trials until the first success occurs.

Tags

CCSS.HSF.BF.A.2